The paper has been actively discussed by the reviewers and the AC (who also carefully read the submission). The rebuttal was also fully exploited. As a summary (with pros+ and cons-): + Relevant problem + Well written and clearly presented + Novel to the best of our knowledge + Original idea that is likely to inform future research + Non-trivial linear algebra result (Prop. 2) whose resulting fast computation is properly illustrated + Favorable comparison with existing approaches (again, with the results well communicated) + Availability of the code (the emphasis on Bo/GPyTorch can toned down as explained in the rebuttal, e.g., "since low-level abstractions/primitives were readily available in Bo/GPyTorch, we have focused on this particular package...") - Insufficient empirical study of the warm-starting strategies (the rebuttal has helped a bit in this respect) (A) - Insufficient empirical study of the choice of the samples/branching factors (the rebuttal was disappointing here, eluding a bit the core questions) (B) - Insufficient empirical study of the impact of the optimizer used (e.g., also zero-th order optimizers) (C) - Missing empirical discussions about Gaussian-Hermite vs. MC quadrature: as discussed in the rebuttal, a comparison should be included in the final version (D) - Discussion of the experimental results not enough in depth, e.g., "It is not clear at this point whether this is because we are not optimizing the increasingly complex multi-step objective well enough or if additional lookahead means increasing reliance on the model being accurate, which is often not the case in practice ." (E) --> the authors should consider a case where the model is correct (e.g., draws from a GP) and properly analyze the phenomenon All in all, the paper is recommended for acceptance. However, I urge the authors to take concrete actions to develop more in-depth studies/ablations for the points A-B-C and E by the time of the final version of the paper. Moreover, the problems (beyond the analysis expected for A-B-C and E) that are left open should be better communicated in the body of the text.